Interior Regularity Criteria for Suitable Weak Solutions of the Navier-Stokes Equations

We present new interior regularity criteria for suitable weak solutions of the 3-D Navier-Stokes equations: a suitable weak solution is regular near an interior point z if either the scaled $${L^{p,q}_{x,t}}$$ -norm of the velocity with 3/p + 2/q ≤ 2, 1 ≤ q ≤ ∞, or the $${L^{p,q}_{x,t}}$$ -norm of the vorticity with 3/p + 2/q ≤ 3, 1 ≤ q < ∞, or the $${L^{p,q}_{x,t}}$$ -norm of the gradient of the vorticity with 3/p + 2/q ≤ 4, 1 ≤ q, 1 ≤ p, is sufficiently small near z.